Preparation

Preheat oven to 425 degrees. Line a baking sheet with parchment or waxed paper. Slice stem and bottom ends from tomatoes. Slice remaining tomato crosswise into rounds 1/2 inch thick. You will need 6 or more nice rounds (see Step 2). If you like, you can cut rounds from 6 different-colored tomatoes. (Use leftover tomato for another recipe.)

Dust a flat surface with flour, and unfold pastry onto the surface. Cut pastry into circles about 1 inch wider than tomato slices. You will need at least 6 circles. (If your tomato slices are small and you can cut more than 6 circles out of the puff pastry, cut more rounds of both tomato and pastry. The important thing is that the pastry circles be close to an inch larger than the tomato slices.)

Transfer pastry to baking sheet. Spread some mascarpone, if using, over each pastry circle. Sprinkle pastry with basil; top with a tomato slice. Pinch edges of pastry up around edges of tomato. Season tomato rounds with salt and pepper. Scatter Parmesan over rounds. Bake until pastry is puffed and golden, 10 to 12 minutes. Serve warm.